To find the equation of the linear function in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).
### Step 1: Find the slope \( m \)
The slope \( m \) is calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Using the points \((-3, -1)\) and \((2, 4)\), we can assign:
- \( (x_1, y_1) = (-3, -1) \)
- \( (x_2, y_2) = (2, 4) \)
Now plug in the values:
\[
m = \frac{4 - (-1)}{2 - (-3)} = \frac{4 + 1}{2 + 3} = \frac{5}{5} = 1
\]
### Step 2: Find the y-intercept \( b \)
We can use one of the points to find the y-intercept, \( b \). Using the slope-intercept form:
\[
y = mx + b
\]
Substituting \( m = 1 \) and using the point \((2, 4)\):
\[
4 = 1(2) + b
\]
\[
4 = 2 + b
\]
\[
b = 4 - 2 = 2
\]
### Final Equation
Now, substituting \( m \) and \( b \) into the equation:
\[
y = 1x + 2
\]
or simply:
\[
y = x + 2
\]
Thus, the equation of the linear function is:
\[
\boxed{y = x + 2}
\]